Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.
Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the...
In this paper we review different meanings of the word intrinsic in statistical estimation, focusing our attention on the use of this word in the analysis of the properties of an estimator. We review the intrinsic versions of the bias and the mean square error and results analogous to the Cramér-Rao inequality and Rao-Blackwell theorem. Different results related to the Bernoulli and normal distributions are also considered.